The present invention generally relates to a device, a system and a method for transferring energy. More specifically, the present invention relates to a device, a system and a method for pumping energy, such as, for example, vibrational energy from a main or a primary system and/or a main structure to an essentially nonlinear attachment, such as, for example, a nonlinear energy sink (hereinafter “NES”). The NES functions as an energy absorber, connects to the main structure as a module and requires no separate connection to a ground. Energy pumping is a one-way, irreversible transfer of the energy to the NES. As a result, the energy does not flow back to the main structure. Transferring the vibrational energy to the NES facilitates vibration and shock attenuation in the main structure following a disturbance, such as, for example, an externally induced disturbance. Further, after spatial confinements of the disturbance in the NES, vibrational energy is efficiently dissipated through a passive means and/or an active means. Moreover, the device resembles a narrow-band device, such as, for example, a classical vibration absorber or a tuned mass damper. However, the device and the system function as a broad-band absorber while attached only to the main structure. The broad-band absorber is derived from an essential nonlinearity of a connecting stiffness which may be achieved either with a mechanical spring or through an active control.
The device, the system and the method transfers energy and/or undesired motion from the main structure following the disturbance. The disturbance may be from, for example, a transient load, such as, for example, a shock or due to maneuvering of the main structure. Maneuvering the main structure typically results in a residual vibration, such as, for example, ringing. The disturbance may also be self-induced as in, for example, a fluid-structure interaction, resulting in a sustained large-amplitude motion, such as, for example, a limit cycle oscillation (hereinafter “LCO”). Generally, the LCO interferes with the performance of a primary role of the main structure. Three strategies for reducing the effect of the disturbance on the main structure are as follows: isolation which reduces the energy reaching the main structure from the disturbance; damping which dissipates the energy from the disturbance within the main structure; and absorption which removes the energy reaching the main structure from the disturbance via an auxiliary device.
Vibration isolation requires the main structure to be at least a single-degree-of-freedom system. An objective of vibration isolation is to reduce a natural frequency or frequencies of the main structure well below the lowest frequency of excitation. As a result, responses to disturbances are attenuated well above the highest natural frequency of interest. Vibration damping limits the magnitude of a resonant response in the steady-state and controls the peak response and decay rate in a transient state.
Vibration absorption requires a minimum of two degrees of freedom with one or more degrees of freedom constituting the main structure while another remaining degree of freedom is a vibration absorber. A passive vibration absorber is commonly known as a tuned mass damper, a passive mass damper, a tuned mass absorber and/or a passive mass absorber.
A harmonic disturbance is associated with a single frequency. The addition of a degree of freedom, such as, for example, the vibration absorber, may reduce and/or may attenuate a response of the main structure at or near the exciting frequency. Attaching a linear vibration absorber to the main structure and tuning the absorber such that its natural frequency is equal to the frequency of the excitation accomplishes the reduction and/or attenuation of the response of the main structure. A mass ratio between a mass of the absorber and a mass of the main structure is typically as small as possible.
When the frequency of the excitation is equal or nearly equal to the natural frequency of the linear vibration absorber, the response of the primary structure is small and the response of the linear vibration absorber is large. As a result, the response is localized to the linear vibration absorber at the driving frequency. However, near the two new natural frequencies of the main structure with the attached linear vibration absorber, the responses of the main structure and the linear vibration absorber are large.
An attenuation band between two resonant peaks is controlled by the mass ratio and damping coefficients of the main structure and the linear vibration absorber. Increased damping makes the main structure more robust to parametric variations and decreases the attenuation efficiency while a higher mass ratio broadens the attenuation band. The linear vibration absorber is primarily a steady-state device. The linear vibration absorber takes the energy input to the main structure at a single frequency and channels the energy to the linear vibration absorber. As a result, the linear vibration absorber protects the main structure. Small changes in the excitation frequency renders the device counter-productive if a new driving frequency is close to one of the two natural frequencies of the main structure and linear vibration absorber that bound the driving frequency.
For impulsive, wide-band loading, the linear vibration absorber has limited utility because the linear vibration absorber results in two resonant regions over which both the primary structure and the linear vibration absorber magnify the input. A nonlinear system can be exploited to improve performance of a vibration absorber beyond that of the linear system.
Nonlinear stiffness elements may improve attenuation characteristics of a vibration absorption system without increasing complexity and/or compromising economics. Nonlinear designs may be designed to give a spatial confinement or a localization and/or an energy pumping which enhances a capacity of the vibration absorption system to attenuate effects of unwanted broadband and/or narrowband disturbances. The energy pumping cannot be achieved by standard linear and/or nonlinear designs.
Other nonlinear vibration absorbers (hereinafter “NVAs”) have been developed, but none were based on the energy pumping concept. Further, the effectiveness of the NVAs in a shock and/or a vibration isolation of a primary structure has been poor except over narrow frequency ranges. The NVAs are designed to operate near linearized natural frequencies or under conditions of an internal resonance between the natural frequencies of the primary structure. A local design of the NVAs is different from nonlinear energy pumping on which the present invention is based.
Therefore, a need exists for a device, a system and a method which transfers the energy from the main structure to a device and/or an attachment during transient resonance captures. A single resonance capture begins with the main structure vibrating at a large amplitude while a motion of a NES mass is comparatively small. However, even at small displacements, a essentially nonlinear spring connecting the NES mass to the primary structure provides some coupling. As a result, the energy begins to flow to the NES while the amplitude of the NES motion increases. The stiffness of the nonlinear spring depends on the deflection of the nonlinear spring. An amplitude and a frequency of NES motion will exist at which the NES can resonate with the main structure. As a result, an impedance match is achieved between the primary structure and the NES, and the energy flows readily into the NES with an attendant reduction in the energy and/or vibration of the primary structure. As the energy is dissipated in the NES by, for example, a passive damper, the amplitude of the NES motion diminishes and the resonance capture and/or corresponding impedance match are lost. As a result, the flow of energy between the primary structure and the NES is greatly reduced. The energy in the NES is confined therein and/or is prevented from returning to the main structure. The NES dissipates the energy trapped therein. Depending upon the dynamics of the primary system, another resonance capture may be reached, and previous scenario repeats.
The transient resonance captures are distinctly different from internal resonance in coupled undamped systems. The internal resonance is a steady state phenomenon that occurs between coupled nonlinear oscillators with no damping and typically results in nonlinear beating whereby the vibrational energy is continuously exchanged between the coupled oscillators. Hence, no irreversible transfer of energy from one oscillator to another oscillator occurs.
Furthermore, a need exists for a device, a system and a method which is an essentially nonlinear module or attachment for attenuating vibrations in main structures and/or structures subjected to dynamic loads, such as, for example, wide-band or narrow-band loads. The device, the system and the method absorbs, confines and dissipates the energy from vibrations in the main structure. The device is an advantage over the present state of the art because the device offers a protective solution for large scale, complex, flexible structures subjected to broad-band excitation.
Additionally, a need exists for a device, a system and a method for pumping vibrational energy from a main structure to the device or the attachment, the NES. Further, a need exists for a device, a system and a method for transferring vibrational energy rapidly from a main structure to the device or the attachment, the NES. Still further, a need exists for a device, a system and a method for dissipating energy confined within the device or the attachment, the NES. Moreover, a need exists for a device, a system and a method for protecting a primary structure by pumping energy from a main structure following a disturbance to the device or the attachment, the NES.